Math

QuestionExpress the system as a vector and matrix equation:
9x1+x23x3=810x2+4x3=0 \begin{array}{r} 9 x_{1}+x_{2}-3 x_{3}=8 \\ 10 x_{2}+4 x_{3}=0 \end{array}

Studdy Solution

STEP 1

Assumptions1. We have a system of two linear equations with three unknowns x1x1, xx, and x3x3. . The first equation is 9x1+x3x3=89x1 + x -3x3 =8.
3. The second equation is 10x+4x3=010x +4x3 =0.

STEP 2

We can write the system of equations as a vector equation by expressing the left-hand side of each equation as a linear combination of vectors, and the right-hand side as a vector.The vector equation can be written asx1[90]+x2[110]+x[4]=[80]x1 \begin{bmatrix}9 \\0 \end{bmatrix} + x2 \begin{bmatrix}1 \\10 \end{bmatrix} + x \begin{bmatrix} - \\4 \end{bmatrix} = \begin{bmatrix}8 \\0 \end{bmatrix}This corresponds to choice C in the problem.

STEP 3

We can also write the system of equations as a matrix equation. In a matrix equation, the coefficients of the variables form a matrix, the variables themselves form a column vector, and the constants on the right-hand side of the equations form another column vector.
The matrix equation can be written as[913010][x1x2x3]=[80]\begin{bmatrix}9 &1 & -3 \\0 &10 & \end{bmatrix} \begin{bmatrix} x1 \\ x2 \\ x3 \end{bmatrix} = \begin{bmatrix}8 \\0 \end{bmatrix}This corresponds to choice B in the problem.

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